A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out. (C) 2004 American Institute of Physics.